A series of waves traveling at 200 m/sec are being generated by a 100 Hz source. A point at the very top of the crest of a certain wave is ____ meters from a corresponding point 3 crests away.
To find the distance between two corresponding points on waves, we need to determine the wavelength. The wavelength (λ) is the distance between two consecutive crest or trough points on a wave.
The formula to calculate the wavelength is given by:
λ = v / f
Where:
λ = wavelength (in meters)
v = velocity of waves (in meters per second)
f = frequency of the source (in hertz)
In this case, the velocity (v) is given as 200 m/sec and the frequency (f) is given as 100 Hz.
Substituting the values into the formula:
λ = 200 m/sec / 100 Hz
Simplifying the expression:
λ = 2 meters
Therefore, the wavelength of the waves is 2 meters.
Now, we need to find the distance between a point at the top of the crest (called a crest point) and a corresponding point 3 crests away.
Since we know the wavelength is 2 meters, we can calculate the distance by multiplying the wavelength by the number of crests:
Distance = number of crests * wavelength
In this case, the number of crests is given as 3:
Distance = 3 * 2 meters
Simplifying the expression:
Distance = 6 meters
Therefore, the point at the very top of the crest of a certain wave is 6 meters away from a corresponding point 3 crests away.